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Free Electromagnetism MCQs with Answers

1,176 Electromagnetism MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.

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Magnetic Flux DensityMagnetic FluxCharged Particle in a Magnetic Field
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1,176 questions · page 42 of 59

821. A charged particle enters a uniform magnetic field with velocity vector making an angle of 30° with the magnetic field. The particle describes a helical trajectory of pitch x. The radius of the helix is:

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: Pitch x = (2 π m v cos 30°) / (q B) = (2 π m v) / (q B) · √3 / 2 ... (1)Radius r = (m v sin 30°) / (q B) = m v / (2 q B) ...

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Correct answer: Option C

822. The current I in the straight conductor varies sinusoidally with time as shown. (A positive value of I is in the direction indicated). At time t1 the induced current in the rectangular loop is clockwise. What is the current in the rectangular loop at time t2 and time t3 respectively?

  • A. Zero; clockwise
  • B. Zero; counterclockwise
  • C. Clockwise; clockwise
  • D. Clockwise; counterclockwise

Explanation: For t2, I is continuously decreasing, so the magnetic field in the downward direction and is decreasing, hence the direction of induced…

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Correct answer: Clockwise; clockwise

823. A large metal sheet carries an electric current along its surface. Current per unit length is λ. Magnetic field near the metal sheet is:

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: Applying Ampere's law∮ B · dℓ = μ₀ (λ ℓ)2 B ℓ = μ₀ λ ℓB = (1/2) μ₀ λ

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Correct answer: Option A

824. A long straight wire carrying a current of 30 A is placed in an external uniform magnetic field of induction 4 x 10^-4 T. The magnetic field is acting parallel to the direction of the current. The magnitude of the resultant magnetic induction in tesla at a point 2.0 cm away from the wire is:

  • A. 10-4
  • B. 3 x 10^-4
  • C. 5 x 10^-4
  • D. 6 x 10^-4

Explanation: Magnetic field due to wireB = μ₀I / 2πr = (4π × 10⁻⁷) / 2π × 30 / (2 × 10⁻²) = 3 × 10⁻⁴ TThis magnetic field will be perpendicular to…

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Correct answer: 5 x 10^-4

825. A uniform but time-varying magnetic field exists in the cylindrical region and is directed into the paper. If the field decreases with time and a positive charge is placed at any point inside the region. Then it moves:

  • A. Along 1
  • B. Along 2
  • C. Along 3
  • D. Along 4

Explanation: ∫ E · dℓ = - π r² dB/dtE × 2πr = + π r² × dB/dt (since dB/dt = -ve)E = +ve∴ assume direction is rightso a charge q moves along 3.

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Correct answer: Along 3

826. A straight conductor of mass m and carrying a current I is hinged at one end and placed in a plane perpendicular to the magnetic field B as shown in the figure. At any moment if the conductor is let free, then the angular acceleration of the conductor will be (neglect gravity):

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: Torquedτ = dF × r = i B dr × rτ = ∫₀ᴸ i B r dr = i B L² / 2α = τ / I = (i B L² / 2) / (2 m L² / 3) = (3/2) i B / m

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Correct answer: Option A

827. A compass needle placed at a distance r from a short magnet in tanA position shows a deflection of 60°. If the distance is increased to r(3)1/3, then the deflection of the compass needle is:

  • A. 30°
  • B. 60° × (3)1/3
  • C. 60° × (3)2/3
  • D. 60° × (3)3/3

Explanation: In tan A position 2kM / r³ = Bₕ tan θ(r₁ / r₂)³ = tan θ₂ / tan θ₁ ⇒ θ₂ = 30°

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Correct answer: 30°

828. A magnetic needle of negligible breadth and thickness compared to its length, oscillates in a horizontal plane with a period T. The period of oscillation of each part obtained on breaking the magnet into n equal parts and perpendicular to the length is:

  • A. T
  • B. T/n
  • C. Tn
  • D. 1/Tn

Explanation: T = 2π √(I / MB)on breaking n equal parts perpendicular to lengthI' = (1/12) (m/n) (ℓ/n)² of each partI' = I / n³ , M' = M / nT' / T =…

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Correct answer: T/n

829. The tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of 60° and 45° respectively. The ratio of the number of turns in the coil is:

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: In series current is same. In tangent galvanometerB = Bₕ tanθ ⇒ μ₀nI / 2R = Bₕ tanθθ I = Same ∴ n ∝ tanθ ⇒ n₁ / n₂ = tan60° / tan45° = √3…

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Correct answer: Option D

830. There is magnetic material of coercivity 2 x 10^3 A/m. What current should flow through the solenoid of length 15 cm having 150 turns to demagnetize the substance completely?

  • A. 4 A
  • B. 2.5 A
  • C. 2 A
  • D. 3.5 A

Explanation: H = 2 × 10³, for solenoid H = n In = 150 / (15 × 10⁻²) = 1000⇒ I = H / n = (2 × 10³) / 10³ = 2 A.

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Correct answer: 2 A

831. Magnetic susceptibility of a substance is - 0.925. What is it's relative permeability?

  • A. 1.935
  • B. 0.075
  • C. 0.175
  • D. 2.375

Explanation: As we know that relation between magnetic susceptibility and relative permeability:µr= 1 + Xm;µr= 1 - 0.925 = 0.075

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Correct answer: 0.075

832. A short bar magnet produces a magnetic induction of 4 x 10^-5 T at an axial point 10 cm from its center. It's dipole moment is (µ0= 4 x 10^-7 Wb / AM):

  • A. 0.2 Am2
  • B. 2 x 10^-5 Am2
  • C. 2 Am2
  • D. None of these

Explanation: At an axial point B = μ₀ / 4π · 2M / r³∴ 4 × 10⁻⁵ = 10⁻⁷ × 2M / 0.001∴ M = 4 × 10⁻⁵ × 0.001 / 2 × 10⁻⁷= 0.2 A·m²

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Correct answer: 0.2 Am2

833. Magnetic field induction due to an infinite long solid cylindrical conductor of radius R at a distance x< R and y>R are equal in magnitude then :

  • A. xy=R2
  • B. xy=R
  • C. x=y
  • D. x/y =R

Explanation: x > R , B = (μ₀ / 4π) · (2I / x)y < R , B′ = (μ₀ / 4π) · (2I y / R²)But B = B′⇒ xy = R²

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Correct answer: xy=R2

834. A coil with a number of turns N, is made from a wire of length l, carrying current I. What will be the magnetic moment of the coil?

  • A. L2I/4πN2
  • B. L2NI/4π
  • C. L2I/4πN
  • D. L2IN2/4π

Explanation: Magnetic moment = NI (πr²)Also 2πrN = ℓ⇒ r = ℓ / (2πN)Magnetic moment = ℓ² I / (4πN).

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Correct answer: L2I/4πN

835. In the figure, a charged sphere of mass m and charge q starts sliding from rest on a vertical fixed circular track of radius R from the position shown. There exists a uniform and constant horizontal magnetic field of induction B. The maximum force exerted by the track on the sphere is:

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: Fₘ = qvB, and directed radially outward.∴ N − mg sin θ − qvB = mv²/R⇒ N = mv²/R + mg sin θ + qvBHence at θ = π/2⇒ Nₘₐₓ = 2mgR/R + mg +…

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Correct answer: Option C

836. Electrons at rest are accelerated by a potential of V volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field B. The radius of the path of the electrons inside the magnetic field is:

  • A. The radius is proportional to the square root of the potential V divided by the magnetic field B
  • B. The radius is proportional to the square root of (2mV/e) divided by the magnetic field B
  • C. The radius is directly proportional to the potential V and inversely proportional to the magnetic field B and charge e
  • D. The radius is directly proportional to the magnetic field B and inversely proportional to the square root of the potential V

Explanation: The gain in K.E. of the electron after moving through the potential differenceV = eV = (1/2) m v²⇒ v = √(2 e V / m)⇒ r = mv / eB = (1/B)…

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Correct answer: The radius is proportional to the square root of (2mV/e) divided by the magnetic field B

837. A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x>b is:

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D

Explanation: Width of the magnetic field region (b − a) ≤ R ; where 'R' is its radius of curvature inside magnetic field.∴ R = mv / qB = (b − a) ⇒ v =…

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Correct answer: Option B

838. A small square loop of wire of side l is placed inside a large square loop of wire of side L(>>l ). The loops are coplanar and their centres coincide. The mutual inductance of the system is:

  • A. Directly proportional to I2
  • B. Inversely proportional to I2
  • C. Directly proportional L2
  • D. Inversely proportional to L2

Explanation: Because of larger loop, the field at the centre will beB = (4 × μ₀ i) / (4π (L/2)) (sin 45° + sin 45°)B = (μ₀ / 4π) (8√2 i / L)So, flux…

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Correct answer: Directly proportional to I2

839. A current I = 10 sin(100π t) amp. is passed in first coil, which induces a maximum e.m.f of 5π volt in second coil. The mutual inductance between the coils is:

  • A. 10 mH
  • B. 15 mH
  • C. 25 mH
  • D. 5 mH

Explanation: Let I = I₀ sin ωt,where I₀ = 10, ω = 100 πthen ε = M dI/dt= M d/dt (I₀ sin ωt)= M I₀ ω cos ωt∴ εₘₐₓ = M I₀ ω5π = M × 10 × 100 πM = 5 mH.

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Correct answer: 5 mH

840. Assertion: After increasing the magnetic flux through induction the self-inductance also increases.Reason: Because the self-inductance is directly proportional to the magnetic flux.

  • A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion
  • B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion
  • C. If Assertion is true statement but Reason is false
  • D. If both Assertion and Reason are false statements

Explanation: The value of the self-inductance will be high if the magnetic flux is stronger for the given value of current.

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Correct answer: If both Assertion & Reason are true and the reason is the correct explanation of the assertion
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